The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X a^2*X a*X  X a^2*X  0 a*X a*X a*X  X  0  0  X  X  0 a^2*X  0  X a*X a^2*X  0  X a*X a*X a*X  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X  0 a*X a^2*X a*X  0  X a*X a^2*X a^2*X a*X  X  X  0  0 a*X  X  X  X  0  X  0 a*X a*X
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X  0 a*X a^2*X  0  0 a*X  X  X a^2*X a^2*X a^2*X  0 a^2*X  X a*X a*X  0  X a*X  0 a*X a*X  0
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X a*X a*X a*X a^2*X  X a*X a*X  0 a^2*X a^2*X  0  X a*X a*X  0  0 a^2*X  0 a*X  X a*X  0 a*X

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 104.

Homogenous weight enumerator: w(x)=1x^0+132x^104+171x^108+183x^112+768x^114+99x^116+2304x^118+135x^120+117x^124+45x^128+57x^132+42x^136+36x^140+3x^144+3x^152

The gray image is a linear code over GF(4) with n=156, k=6 and d=104.
This code was found by Heurico 1.16 in 0.109 seconds.